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Basic Trigonometry
Revision Notes
𝐬𝐒𝐧 𝒙 =
𝒐𝒑𝒑
𝐜𝐨𝐬 𝒙 =
π’‰π’šπ’‘
𝒂𝒅𝒋
𝐭𝐚𝐧 𝒙 =
π’‰π’šπ’‘
𝒐𝒑𝒑
𝒂𝒅𝒋
x = angle
hyp = hypotenuse(side opposite to the right angle)
opp = opposite(side opposite to the non-right angle given in the question or opposite to the
angle you are trying to find).
adj = adjacent(side next to the non-right angle given in the question or opposite to the angle
you are trying to find).
Using Basic Trigonometry to find the length of a missing side
e.g.
hyp
opp
14.6cm
a
37o
adj
Label the sides.
Select the rule. To do this you need to look at what side you are trying to find. In this
example it is the opposite side. You then need to see which other side you know the length
of. In this example you know that the hypotenuse is 14.6cm. You need to select the rule
that contains these two sides. For this example therefore you need to use –
𝐬𝐒𝐧 𝒙 =
𝒐𝒑𝒑
π’‰π’šπ’‘
You now need to substitute the known values into the rule.
𝐬𝐒𝐧 πŸ‘πŸ• =
𝒂
πŸπŸ’. πŸ”
Rearrange the equation to find a.
𝒂 = πŸπŸ’. πŸ” × π’”π’Šπ’πŸ‘πŸ•
𝒂 = πŸ–. πŸ•πŸ—π’„π’Ž(πŸπ’…π’‘)
Using Basic Trigonometry to find a missing angle
e.g.
hyp
opp
12.2cm
x
7.8cm
adj
Label the sides.
Select the rule. To do this you need to look at what sides you know the length of. In this
example you know that the adjacent is 7.8cm and hypotenuse is 12.2cm. You need to select
the rule that contains these two sides. For this example therefore you need to use –
𝐜𝐨𝐬 𝒙 =
𝒂𝒅𝒋
π’‰π’šπ’‘
You now need to substitute the known values into the rule.
𝐜𝐨𝐬 𝒙 =
πŸ•. πŸ–
𝟏𝟐. 𝟐
Rearrange the equation to find x.
𝒙 = πœπ¨π¬βˆ’πŸ (
πŸ•. πŸ–
)
𝟏𝟐. 𝟐
𝒙 = πŸ“πŸŽ. πŸπŸ”π’ (πŸπ’…π’‘)
Key Points
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Basic Trigonometry can only be used on right angle triangles. If the question does
not contain a right angle triangle, then you cannot use Basic Trigonometry to answer
it!
Basic Trigonometry can be used to find a missing side if you are given another side
and at least one of the angles.
Basic Trigonometry can also be used to find a missing angle if you are given at least
two of the sides.
Remember if you are finding a missing side and are given the other two sides, you
should use Pythagoras’ Theorem to find the answer.
Don’t forget to include units on your answer.
Be careful when using your calculator. Make sure you enter the values in the correct
order depending on your calculator.
Exam Questions
Q1.
Calculate the value of x.
Give your answer correct to 3 significant figures.
.......................................................................................................................................
(Total for Question is 3 marks)
Q2.
Diagram NOT accurately drawn
LMN is a right-angled triangle.
MN = 9.6 cm.
LM = 6.4 cm.
Calculate the size of the angle marked x°.
Give your answer correct to 1 decimal place.
. . . . . . . . . . . . . . . . . . . . . .°
(Total for Question is 3 marks)
Q3.
ABCD is a parallelogram.
DC = 5 cm
Angle ADB = 36°
Calculate the length of AD.
Give your answer correct to 3 significant figures.
.......................................................................................................................................
(Total for Question is 4 marks)
Q4.
* The diagram shows a ladder leaning against a vertical wall.
The ladder stands on horizontal ground.
The length of the ladder is 6 m.
The bottom of the ladder is 2.25 m from the bottom of the wall.
A ladder is safe to use when the angle marked y is about 75°.
Is the ladder safe to use?
You must show all your working.
(Total for Question is 3 marks)
Past Paper Question
Mock Exam Question